Barnsley, who conceded five goals in their loss at home to Watford last weekend, played a defensive-minded 5-4-1 formation and frustrated the home side throughout a goalless first half.
However, Jack Butland - making his debut for the Tykes following a loan move from Stoke City - had to be alert to deny Danny Drinkwater, Lloyd Dyer and Luke Varney in quick succession in the opening 45 minutes.
On the stroke of half time, the travelling support appealed loudly for a penalty after Jean Yves Mvoto was felled in the 18-yard box, but the referee waved away the protests.
For all Barnsley's good work, it took the Foxes just five minutes of the second half to break the deadlock. Dyer wriggled free on the right wing and fed former England striker Nugent, who finished well to score his first goal from open play this season.
Leicester continued to push for a second goal, and Butland produced an acrobatic save before Scott Wiseman nodded Drinkwater's header off the line.
Nugent scored his fifth penalty of the season to double his side's lead in the 61st minute after Mvoto's rash challenge inside the box.
The final 15 minutes saw Leicester with their backs to the wall as Barnsley pushed and probed for an equaliser.